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Calculate the coefficient of correlation between x & y from the following data.
x 23 27 28 29 30 31 33 35 36 39
y 18 22 23 24 25 26 28 29 30 32

1 Answer
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Let us assume $\bar {X}$ = 30 & $\bar{Y}$= 25

Given N=10

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r= $\frac{\sum{dxdy}- \frac{(\sum{dx})(\sum{dy})}{N}}{(\sqrt{\sum{dx^2}-\frac{(\sum{dx})^2}{N}})(\sqrt{\sum{dy^2}-\frac{(\sum{dy})^2}{N}})}$

r= $\frac{186- (\frac{11\times 7}{10})}{(\sqrt{215-\frac{(11)^2}{10}})(\sqrt{163-\frac{(7)^2}{10}})}$

r= $\frac{186- 7.7}{\sqrt{215- 12.1}\sqrt{163-4.9}}$

r= $\frac{178.3}{\sqrt{202.9}\sqrt{158.1}}$

r= 0.9948

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